An Introduction to Quantum Stochastic Calculus
An Introduction to Quantum Stochastic Calculus
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DOI：
10.1007/978-3-0348-8641-3
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发表时间：
1992
期刊：
影响因子：
--
通讯作者：
K. Parthasarathy
中科院分区：
文献类型：
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作者：
K. Parthasarathy
《量子随机微积分导论》旨在从经典和量子的角度加深我们对受机会定律支配的系统动力学的理解，并促进它们统一的进一步研究。这可能是第一次系统地尝试将经典概率论编织到量子框架中，并提供了大量有趣的特征：伊藤对布朗运动和泊松过程的修正公式的起源可以追溯到对易关系，或者同等地，不确定性原理。量子随机积分使观察费米子和玻色子场之间的新关系成为可能。许多量子动力半群和经典马尔可夫半群都是通过幺正算子演化实现的。文本几乎是自成一体的，只需要在研究生水平的算子理论和概率论的基本知识。这是一本极好的书，无论是对已经在这个领域活跃的人还是对这个领域的新手来说，它都将是一个有价值的伴侣。此外，有大量的刺激练习分散在文本中，这将是非常宝贵的学生。（数学评论）本专著通过强调量子形式主义的数学方面及其与经典概率的联系，并通过精心挑选的泛函分析材料的广泛呈现，系统而独立地介绍了Fock空间量子随机演算的基本形式（…）。这使得这本书对于概率论方向的读者来说非常方便，希望了解非交换概率的奇迹，更具体地说，对于学习这个领域的数学学生来说。文笔优美，对高等数学的精妙之处有明显的欣赏（…）最引人注目的是作者将经典概率论编织到量子框架中的努力。（美国数学月刊）
An Introduction to Quantum Stochastic Calculus aims to deepen our understanding of the dynamics of systems subject to the laws of chance both from the classical and the quantum points of view and stimulate further research in their unification. This is probably the first systematic attempt to weave classical probability theory into the quantum framework and provides a wealth of interesting features: The origin of Ito’s correction formulae for Brownian motion and the Poisson process can be traced to commutation relations or, equivalently, the uncertainty principle. Quantum stochastic integration enables the possibility of seeing new relationships between fermion and boson fields. Many quantum dynamical semigroups as well as classical Markov semigroups are realised through unitary operator evolutions. The text is almost self-contained and requires only an elementary knowledge of operator theory and probability theory at the graduate level.---This is an excellent volume which will be a valuable companion both to those who are already active in the field and those who are new to it. Furthermore there are a large number of stimulating exercises scattered through the text which will be invaluable to students.(Mathematical Reviews) This monograph gives a systematic and self-contained introduction to the Fock space quantum stochastic calculus in its basic form (...) by making emphasis on the mathematical aspects of quantum formalism and its connections with classical probability and by extensive presentation of carefully selected functional analytic material. This makes the book very convenient for a reader with the probability-theoretic orientation, wishing to make acquaintance with wonders of the noncommutative probability, and, more specifcally, for a mathematics student studying this field.(Zentralblatt MATH) Elegantly written, with obvious appreciation for fine points of higher mathematics (...) most notable is [the] author's effort to weave classical probability theory into [a] quantum framework.(The American Mathematical Monthly)